Question

Consider the following mortgage: Loan amount $376,038 30 year maturity with monthly payments Fully amortizing Fixed interest rate at 5% Suppose the investors use 50% PSA model to predict prepayments. What would be their prediction for the dollar amount of prepayments in the first month? Round your answer to the nearest cent (e.g. if you answer is $1,400.677777, write 1400.68).

Answer 1

Given Information

Loan Amount (P) = $376,038

Time (in months) (N) = 30 * 12 = 360

Interest Rate (per month) (r) = 5%/12 = 0.417% = 0.00417

Formula for monthly payments (EMI) –

EMI = [P * r * (1+r)^N ] / [(1+r)^N – 1]

So, EMI = [376038 * 0.00417 * (1+0.00417)³⁶⁰ ] / [(1+0.00417)³⁶⁰ – 1]

=> EMI = $2018.65 per month

For 1^st month, following table gives the details –

­­Month	Opening Principal Balance	EMI	Interest	Principal Repayment	Closing Principal Balance
1	376,038.00	2,018.65	1,566.83	451.83	375,586.17

CPR (Conditional Prepayment Rate) for 1^st month is 0.2% per annum which increases by 0.2% per month upto 30 months and then 6% for months 30 to 360.

So, CPR (month 1) = 1 * 0.2% = 0.2%

50% PSA = 0.5 * 0.2% = 0.1% = 0.001

SMM (Single Monthly Mortality Rate) = 1 – (1-CPR)^1/12

So, SMM (month 1) = 1 – (1-0.001)^1/12 = 0.0000834 or 0.00834%

Now, for a particular month

Prepayment = SMM * (Mortgage balance at the beginning of month – Scheduled principal payment for the month)

=> Prepayment (month 1) = 0.0000834 * (376,038.00 -451.83) = $31.31